Does the term “lunation” fit more with words like lunatic and lunacy or with words like lunar and lunate? As you might guess, given this author is an astrophysicist, it’s the latter—terms related to the Moon. This etymological similarity isn’t a coincidence, by the way, since the former terms have roots in beliefs about the Moon being linked to insanity. But we’re sticking with the Moon side of things here.
A lunation refers simply to the period of time between successive new moons, or the length of time it takes the Moon to pass through all of its phases, and it is also known as a synodic month, in contrast to a sidereal month, which is the time it takes the Moon to return to the same position relative to distant stars. The average lunation is 29.530590278 days, but any individual lunation might vary from that amount by several hours. In fact, if we look at how the duration of lunations vary over time, we can see a very regular pattern.
Specific lunations can be designated by calendar dates, but are often referred to by their Brown Lunation Number (BLN), a numbering system developed by astronomer Ernest William Brown where lunation 1 is taken to be the lunation starting January 17, 1923. That makes the lunation beginning in October 2024 lunation 1259, which is 29.748611 days long. This is actually a (local) peak in length, and the following lunations will start decreasing in length until a minimum duration is reached for lunation 1267 in May 2025. (Lunation 1259 also happens to be the lunation of the very first edition of The Gibbous Guide, which you can subscribe to here to get more fun astronomy in your inbox!)
The cause of this behavior is a complex interplay of orbital dynamics between the Moon, Earth, and Sun. If the Moon and Earth were an isolated two-body system, every lunation would have the exact same length. In fact, it wouldn’t even really be a lunation because the Moon wouldn’t have phases, and there wouldn’t be any distinction between a synodic month and a sidereal month. Add in the Sun, and things get a lot more interesting!
Because Earth orbits the Sun, it has moved along its orbit during the time it takes the Moon to complete a sidereal orbit. To get back to the same position relative to the Sun, the Moon needs to go a little bit further—this is why a synodic month is longer than a sidereal month. But this doesn’t explain why the length of the synodic month varies. For that, we need to look more closely at the orbits of both the Moon and Earth.
The Moon’s orbit is eccentric. Not by much, it has an eccentricity of just 0.0549. That means the long axis of the Moon’s orbit is just over 11% longer than the short axis of its orbit. Visually, it’s hard to even discern it isn’t a circle, but it isn’t! This means that the Moon’s orbit has an apogee and a perigee, points furthest and closest to Earth, respectively.
The location of the Moon in its orbit can be given by its true anomaly, which is basically the angle it makes to the location of perigee. Now because we know the Moon has to go a bit past one full sidereal orbit in order to complete a synodic month, that means the true anomaly at the new moon changes for each lunation. If the true anomaly of the new moon is near apogee, the synodic month will be longer because that “extra” piece the Moon has to travel is longer and because the Moon is traveling slower near apogee. (This change in velocity is a property of orbits described by Kepler’s Second Law and will be the subject of its own post in the future!)
Thus if we look at the change in the length of a lunation over time compared to the change in the true anomaly of the Moon at the new moon, they change together at the same period, which is about 1.13 years. A keen reader may be wondering why that period isn’t one year, when the Sun’s location relative to Earth would be back to the same position.
The reason is because the orientation of the Moon’s orbit is changing over time! Again, if Earth and the Moon were a simple two-body system, this wouldn’t happen, but gravity from the Sun nudges the Moon’s orbit, leading to the location of perigee changing over time. So as Earth orbits and returns to the same position relative to the Sun, the Moon’s orbit has turned such that another approximately 47 days are needed for the orientation of the Moon’s orbit to be back in the same position relative to the Sun.
This has all been pretty complicated already, but that’s just explaining the short-term variation of the lunation. If we zoom out in time, we can see that there is another, longer-term periodic behavior on top of these short-term variations!
This is because Earth’s orbit is also eccentric. It’s not quite as eccentric as the Moon’s, with an eccentricity of 0.0167, but even that small deviation from circularity has effects. Earth also follows Kepler’s Second Law and moves faster at its perihelion than at its aphelion.
This means that during the course of a sidereal month, Earth moves farther along its orbit at perihelion, meaning the Moon has further to travel to complete a lunation. Thus the lunations increase at perihelion and decrease at aphelion. And the size of this effect also varies depending on the orientation of the Moon’s orbit relative to Earth’s orbit. When the Moon’s perigee aligns with Earth’s perihelion, the effect is strongest, and it’s weakest when the Moon’s apogee aligns with Earth’s perihelion. Thus while lunation 1259 is the longest lunation when we look at a year or so, it’s still over an hour and a half shorter than, for example, lunation 1286 in December 2026.
And even considering all of the above, there are still additional effects that we are neglecting to include, like the fact that the eccentricity of both the Moon’s orbit and Earth’s orbit change over time and …
You can see why the three-body problem is, indeed, a problem! Even apparently simple systems like Earth-Moon-Sun exhibit complex variability from the gravitational interactions of the three objects.
Data from:
- https://aa.usno.navy.mil/data/MoonPhases for the new moon dates (lunation starts)
- https://ssd.jpl.nasa.gov/horizons/app.html#/ for the Moon’s true anomaly